What is the differential equation of all parabolas of the type y^2 = 4a (x - b)?

$y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0$

$ \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0 $

$ \frac{d^2 y}{d x^2}+x^2\left(\frac{d y}{d x}\right)^2=0$

$y^2 \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0 $

What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?

y = 2tan$\left(\frac{x}{2}\right)$ − x + c

y = tan$\left(\frac{x}{2}\right)$ − x + c

y = $\frac{1}{2}\tan\left(\frac{x}{2}\right)$ − x + c

y = tan$\left(\frac{x}{2}\right)$ − 2x + c

Differential Equations — NDA Previous Year Questions

30 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 30
Years covered: 2021–2025
Avg / year: ~6
Subject: Mathematics

How many NDA questions come from Differential Equations?

Differential Equations has contributed 30 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 6 questions a year. That count is measured from EByAi’s bank of 15,695 NDA questions, not estimated from a syllabus. Every one of the 30 questions carries a written, step-by-step solution, and each is tagged to Differential Equations within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Differential Equations questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 30 Differential Equations questions (with full written solutions) are available in practice.

Question 1 · NDA 2024
What is the solution of the differential equation?
1. (A) $y^4 + 2x = c$
2. (B) $y^4 + 3x = c$
3. (C) $2xy^4 + x = c$
4. (D) $4xy - y^4 = c$
Show answerAnswer
$Answer: (D) 4xy - y^4 = c$
Question 2 · NDA 2024
What are the order and degree respectively of the differential equation?
1. (A) $1 and 1$
2. (B) $1 and 2$
3. (C) $2 and 1$
4. (D) $1 and 3$
Show answerAnswer
$Answer: (A) 1 and 1$
Question 3 · NDA 2023
What is the length of latus rectum of the parabola?
1. (A) $1$
2. (B) $\frac{1}{2}$
3. (C) $\frac{1}{4}$
4. (D) $\frac{1}{8}$
Show answerAnswer
$Answer: (B) \frac{1}{2}$
Question 4 · NDA 2023
What is the differential equation of all parabolas of the type y^2 = 4a (x - b)?
1. (A) $\frac{d ^{2} y}{d x ^{2}} + (\frac{d y}{d x})^{2} = 0$
2. (B) $\frac{d ^{2} y}{d x ^{2}} + x^{2} (\frac{d y}{d x})^{2} = 0$
3. (C) $y^{2} \frac{d ^{2} y}{d x ^{2}} + (\frac{d y}{d x})^{2} = 0$
4. (D) $y \frac{d ^{2} y}{d x ^{2}} + (\frac{d y}{d x})^{2} = 0$
Show answerAnswer
$Answer: (D) y \frac{d ^{2} y}{d x ^{2}} + (\frac{d y}{d x})^{2} = 0$
Question 5 · NDA 2022
What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?
1. (A) $y = tan (\frac{x}{2}) - x + c$
2. (B) $y = \frac{1}{2} tan (\frac{x}{2}) - x + c$
3. (C) $y = 2tan (\frac{x}{2}) - x + c$
4. (D) $y = tan (\frac{x}{2}) - 2x + c$
Show answerAnswer
$Answer: (C) y = 2tan (\frac{x}{2}) - x + c$

Differential Equations questions by year

Year	Questions	Share of chapter questions
2025	3
2024	6
2023	7
2022	6
2021	8

Practise these 30 questions with solutions

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FAQs

How many NDA questions have been asked from Differential Equations?

EByAi's bank holds 30 real NDA questions from Differential Equations, asked between 2021 and 2025 — about 6 per year on average. Every count is measured from actual papers, not estimated.

Is Differential Equations important for NDA?

30 questions over 5 papers make Differential Equations a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Differential Equations PYQs online for free?

Yes. EByAi lets you solve NDA past-year questions in the browser with written solutions — free daily practice, no card needed.

More NDA Mathematics chapters

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